The equation of ellipse x²/16 + y²/9 = 1

 

Let the point P on the ellipse be (4cos(theta), 3sin(theta)), then the slope of the tangent is give by 

 

 

-3cos(theta)/4sin(theta)= tan(135⁰)=-1

 

tan(theta)=3/4

 

cos(theta)=4/5

 

sin(theta)=3/5

 

Therefore, the coordinate of the point P is ( 4*(4/5), 3*(3/5))=(16/5, 9/5)